Question

In the rectangular coordinate system, line \(k\) passes through the points (0,0) and (4,8); line \(m\) passes through the points (0,1) and (4,9).

Column A	Column B
The slope of line \(k\)	The slope of line \(m\)

 

Hint:

The slope represents the "rise over run." For both lines, the "run" (change in x) is \(4 - 0 = 4\). The "rise" (change in y) for line k is \(8 - 0 = 8\), and for line m is \(9 - 1 = 8\). Since both have the same rise and the same run, their slopes must be identical without needing to complete the division.

Answer 1

Step 1: Understanding the Concept:
This question asks us to calculate and compare the slopes of two lines, given two points on each line.
Step 2: Key Formula or Approach:
The formula for the slope (\(m\)) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \] Step 3: Detailed Explanation:
For Column A: The slope of line k
The points are (0,0) and (4,8).
Let \((x_1, y_1) = (0,0)\) and \((x_2, y_2) = (4,8)\).
\[ \text{slope of } k = \frac{8 - 0}{4 - 0} = \frac{8}{4} = 2 \] For Column B: The slope of line m
The points are (0,1) and (4,9).
Let \((x_1, y_1) = (0,1)\) and \((x_2, y_2) = (4,9)\).
\[ \text{slope of } m = \frac{9 - 1}{4 - 0} = \frac{8}{4} = 2 \] Step 4: Final Answer:
Both lines have a slope of 2. Therefore, the two quantities are equal. The lines are parallel.